In Chapter 5 we have shown that there are various classes of inflationary kinematics, and we have stressed that the kinematic properties of the string cosmology backgrounds may be very different from the “standard” kinematic properties typical of field theory models of inflation. A question which naturally arises is whether such kinematic differences may correspond (at least in principle) to observable phenomenological differences, suitable to provide a clear signature of the various primordial scenarios.

The answer to this question is positive, as the transition from accelerated to decelerated (i.e. from inflationary to standard) evolution amplifies the quantum fluctuations of the various background fields, and may produce a large amount of various species of radiation. The spectral properties of this radiation, on the other hand, are strongly correlated to the kinematics of the inflationary phase, as we shall see in this chapter. A direct (or indirect) observation of such a primordial component of the cosmic radiation may thus give us important information on the inflationary dynamics, testing the predictions of the various cosmological scenarios.

This chapter is devoted to the study of the direct inflationary production of gravitational radiation, starting from the amplification of the tensor part of the metric fluctuations and the subsequent formation of a cosmic background of relic gravitons. Such a background, if produced at curvature scales H ≲ MP, is expected to survive almost unchanged till the present epoch, thus transmitting to us (encoded inside its spectral structure) a faithful imprint of the primordial kinematics [1].